Rank decomposition and symmetric rank decomposition over arbitrary fields

2021/05/31 by Riguang Huang, Baodong Zheng, Xiaoyu Song · 1 citation
Mathematics · Medicine · Engineering · #Tensor decomposition and applications #Advanced Neuroimaging Techniques and Applications #Sparse and Compressive Sensing Techniques

paper · doi:10.1080/03081087.2021.1935436

Abstract

We give a necessary and sufficient condition for symmetric tensors to have symmetric rank decompositions and give some further results on the Comon's Conjecture (i.e. the rank and symmetric rank agree for a symmetric tensor). In particular, as an application, we prove that if an m-order 2-dimensional symmetric tensor has a symmetric rank decomposition, then its symmetric rank equals its rank or its rank plus one.

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